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Thank you for your suggestions.
In my previous message I did not share too much detail, now I try to better explain what I did.
I made some changes to adapt the project to my needs, I used an standard Arduino uno module and I made a shield with on top the necessary components wired in a standard way, without any PCB.
The photos clarify better what I did.
The important part of the structure remained unchanged, I changed only the platform base.
Hall sensor and Mosfet are those used by you.
I think the problem is the coil, maybe the wire is too big and therefore there are less turns.
I did a lot of tests, the only decent levitation I obtained was with two 10x10 magnets on top of the bolt and with a very large levitation magnet, it is 20x20x10 and weighs about 30 grams.
I do not have problems for the power supply because I have used a laboratory power supply for testing and therefore I am sure of the quality of the voltage.
I tried with voltages from 12 to 20 volts.
Obviously the power supply circuit was modified, the input voltage goes to a DC / DC traco power regulator with 12/24 Volt input and 9 Volt output, there is also a 100uF capacitor on the output.
The 9 Volt is used to power the Arduino module, while the input voltage power only the coil, so I can test whatever voltage I want try.
The voltage is stable and clean, I believe that the problem may be the section of the copper wire.
I'll have to do another reel ....
I did not take many pictures, but I think that what I have shared is enought to have an idea.
The levitation is here but non very stable and not reliable.
As you can see from the monitor screen shoot the control is not regular and is too much nervous, obviously I tried may setup with PID values but is very very wearying.
Any other suggestion are really very wellcome